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Question

A five digit number is formed by the digits 1, 2, 3, 4, 5, 6 and 8.  The probability that the number has even digit at both ends is:
 
  1. None
  2. 37
  3. 27
  4. 47


Solution

The correct option is C 27
Total number of 5 digit numbers obtained by the digits 1, 2,3,4,5,6 and 8
=7P5=7.6.5.4.3=2520.
There are 4 even digits (2, 4, 6 and 8).
2 even digits can be selected in
4C2=6 ways 
The two ends can be filled in
2×6=12 ways.
Remaining 3 places from remaining 5 digits can be filled in 5P3=60 ways
Hence the required probability =12×602520=27
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